Here, α, β, and γ are the angles at the center of the sphere subtended by the three arcs of the spherical surface triangle a, b, and c, respectively.

( Here α and β are real and i represents the imaginary unit.

Here, β is a function of the geometry of the space-time in which the string moves.

Here ω < sup > α </ sup >< sub > β </ sub > defines a k × k matrix of one-forms on U. In fact, given any such matrix the above expression defines a connection on E restricted to U. This is because ω < sup > α </ sup >< sub > β </ sub > determines a one-form ω with values in End ( E ) and this expression defines ∇ to be the connection d + ω, where d is the trivial connection on E over U defined by differentiating the components of a section using the local frame.

Here, a, b, and c are the angles at the centre of the sphere subtended by the three sides of the triangle, and α, β, and γ are the angles between the sides, where angle α is opposite the side which subtends angle a, and so forth.

Here, (( α → β ) → α ) is the type of the function f, which can either return a value of type α directly or apply an argument to the continuation of type ( α → β ).

Here, β = 1 / kT, where k is Boltzmann's constant, and T is the temperature.

Here x and t are spacetime coordinates, (,) is the Killing form of a real r-dimensional Cartan algebra of a Kac-Moody algebra over, α < sub > i </ sub > is the i < sup > th </ sup > simple root in some root basis, n < sub > i </ sub > is the Coxeter number, m is the mass ( or bare mass in the quantum field theory version ) and β is the coupling constant.

is symmetric in s and t. Here β is the Bockstein operation and ( Ad β ) P

Here the capacitance of capacitor C1 is multiplied by the transistor's current gain ( β ).

Here, < sub > n </ sub > denotes the sample mean of the first n samples ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >), s < sup > 2 </ sup >< sub > n </ sub > their sample variance, and σ < sup > 2 </ sup >< sub > n </ sub > their population variance.

Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).

Here K denotes the field of real numbers or complex numbers, I is a closed and bounded interval b and p, q are real numbers with 1 < p, q < ∞ so that

Here k is first-order rate constant having dimension 1 / time, ( t ) is concentration at a time t and < sub > 0 </ sub > is the initial concentration.

Here I < sub > 2 </ sub > is reduced to I < sup >–</ sup > and S < sub > 2 </ sub > O < sub > 3 </ sub >< sup > 2 –</ sup > ( thiosulfate anion ) is oxidized to S < sub > 4 </ sub > O < sub > 6 </ sub >< sup > 2 –</ sup >.

The simplest, and original, implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime and g is primitive root mod p. Here is an example of the protocol, with non-secret values in < span style =" color: blue "> blue </ span >, and secret values in < span style =" color: red "> boldface red </ span >:

Here is the center of the ellipse, and is the angle between the < math > X </ Math >- axis and the major axis of the ellipse.

Here C < sub > p </ sub > is the heat capacity at constant pressure and α is the coefficient of ( cubic ) thermal expansion

Here ( Z / 2Z ) is the polynomial ring of Z / 2Z and ( Z / 2Z )/( T < sup > 2 </ sup >+ T + 1 ) are the equivalence classes of these polynomials modulo T < sup > 2 </ sup >+ T + 1.

Here the kets and columns are identified with the vectors of V and the bras and rows with the dual vectors or linear functionals of the dual space V < sup >*</ sup >, with conjugacy associated with duality.

Here, R < sub > ij </ sub > is the Ricci tensor.

# If A is a cartesian product of intervals I < sub > 1 </ sub > × I < sub > 2 </ sub > × ... × I < sub > n </ sub >, then A is Lebesgue measurable and Here, | I | denotes the length of the interval I.

: Here N ( 0 ) is the electronic density of states at the Fermi energy.

Improv comedy techniques have also been used in television and stand-up comedy, in hit shows such as the recent HBO television show Curb Your Enthusiasm created by Larry David, the UK Channel 4 and ABC television series Whose Line Is It Anyway ( and its spinoffs Drew Carey's Green Screen Show and Drew Carey's Improv-A-Ganza ), Nick Cannon's improv comedy show Wild ' N Out, and Thank God You're Here.

Here, the sum is taken over all different states under permutations p acting on N elements.

Here, there are four energy levels, energies E < sub > 1 </ sub >, E < sub > 2 </ sub >, E < sub > 3 </ sub >, E < sub > 4 </ sub >, and populations N < sub > 1 </ sub >, N < sub > 2 </ sub >, N < sub > 3 </ sub >, N < sub > 4 </ sub >, respectively.

For example, the notion of gauge invariance forms the basis of the well-known Mattis spin glasses, which are systems with the usual spin degrees of freedom for i = 1 ,..., N, with the special fixed " random " couplings Here the ε < sub > i </ sub > and ε < sub > k </ sub > quantities can independently and " randomly " take the values ± 1, which corresponds to a most-simple gauge transformation This means that thermodynamic expectation values of measurable quantities, e. g. of the energy are invariant.

Simmons joined Kid Rock's 2008 Rock N Roll Revival Tour, performing " It's Like That ", " It's Tricky ", " You Be Illin '", " Run's House ", " Here We Go ", " King of Rock " and " Walk This Way " with Kid Rock.

Here Q – the size of message block to be inserted ; N – the size ( in bits ) of one sample of the message file ( see figure The Fourth Protection Level Scheme ).

Here N < sub > x </ sub > is the number of x atoms per volume, λ the electron escape depth, θ the analyzer angle, T the transmission of the analyzer, I ( t ) the electron excitation flux at depth t, dΩ the solid angle, and δt is the thickness of the layer being probed.

which is natural in the variable N. Here the functor Hom ( N, F –) is the composition of the Hom functor Hom ( N, –) with F. This isomorphism is the unique one which respects the limiting cones.

The music then commenced with short sets from bands that were influenced by the music of Queen, including Metallica, Extreme ( playing a Queen medley ), Def Leppard ( who brought Brian May onstage for a faithful version of " Now I'm Here "), and Guns N ' Roses.

Here N < sub > m </ sub > denotes the number of turns in loop m, Φ < sub > m </ sub > the magnetic flux through this loop, and L < sub > m, n </ sub > are some constants.

Here the user specifies a desired frequency response, a weighting function for errors from this response, and a filter order N. The algorithm then finds the set of N coefficients that minimize the maximum deviation from the ideal.

Here is called a spherical harmonic function of degree ℓ and order m, is an associated Legendre polynomial, N is a normalization constant, and θ and φ represent colatitude and longitude, respectively.

They played an unplugged version of " Here Comes the Rain Again ", " 7 Seconds " with Youssou N ' Dour and " Sweet Dreams ".

He has also released an album with Vado entitled Cam ' ron & The U. N. Presents: " Heat in Here " Vol.

( Here, we have used the fact that N < sub > 1 </ sub >< sup >− 1 </ sup > N < sub > 1 </ sub > is unity when evaluated modulo N < sub > 2 </ sub > in the inner sum's exponent, and vice-versa for the outer sum's exponent.

Here the last product means that a first electron, r < sub > 1 </ sub >, is in an atomic hydrogen-orbital centered at the second nucleus, whereas the second electron runs around the first nucleus.

Here the expression has the value 1 if m = 0 and 0 otherwise ( Iverson bracket ).

Here, we have < tt >( λx. xx )( λx. xx ) → ( xx ):= λx. xx = ( x := λx. xx )( x := λx. xx ) = ( λx. xx )( λx. xx )</ tt >.

Here Mavrodes ' worry about X = " to make something its maker cannot lift " will no longer be a problem because " God does X " is not logically consistent.

< center >< span style = " font-variant: small-caps "> Here were buried the remains of

Here for real a, b and c, if Δ > 0, the polynomial has two real roots, if Δ = 0, the polynomial has one real root, and if Δ < 0, the polynomial has no real roots.

Here are the concrete instances of these equations for n = 2 and n = 3:

Here only the digit 9 is replaced by the digit 0, such that identities like 1. 000 ... = 0. 999 ... can spoil the result.

Here orthogonality is important not only for reducing A < sup > T </ sup > A = ( R < sup > T </ sup > Q < sup > T </ sup >) QR to R < sup > T </ sup > R, but also for allowing solution without magnifying numerical problems.

Here a and l denote radius and length of the wire, and Y is a constant that depends on the distribution of the current in the wire: Y =

Here F = J + I, where I is the nuclear spin.

Here the substitution function ( v < sub > 1 </ sub >,..., v < sub > n </ sub >) =

Here the solution was assumed to have the special form Y ( θ, φ ) = Θ ( θ ) Φ ( φ ).

Here the polynomial z < sup > 2 </ sup > − 1 vanishes when z =

Here the sets A and B that contain a and b are calculated recursively, with n = 1 and n = 2 being the base case.

Here H = Hubble constant, ρ

: Here AB = 0, BA = B.

Here, g and g ′ are SU ( 2 ) and U ( 1 ) gauge couplings and tanθ < sub > W </ sub > =

Here the sign of the distances is taken negative if and only if the line segment DX ( X = F, G, H ) lies completely outside the triangle.

for any torsion sheaf F. Here j is any open immersion of X into a scheme Y with a proper morphism g to S ( with f = gj ), and as before the definition does not depend on the choice of j and Y. Cohomology with compact support is the special case of this with S a point.